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Thermal Engineering

Common Thermal Efficiency Equations

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Carnot Efficiency

The equation for Carnot efficiency is

\eta_{\text{Carnot}} = 1 - \frac{T_C}{T_H}

where

T_C

is the absolute temperature of the cold reservoir and

T_H

is the absolute temperature of the hot reservoir. The Carnot efficiency represents the maximum possible efficiency that any heat engine can achieve, operating between two temperatures.

Refrigerator Coefficient of Performance (COP)

The Coefficient of Performance for refrigerators is given by

\text{COP}_{\text{refrigerator}} = \frac{Q_L}{W}

where

Q_L

is the heat extracted from the cold reservoir and

W

is the work input. The COP indicates how efficiently a refrigerator transfers heat from the cold interior to the warmer exterior environment.

Rankine Efficiency

The Rankine cycle efficiency equation is

\eta_{\text{Rankine}} = 1 - \frac{Q_L}{Q_H}

where

Q_L

is the heat rejected in the condenser and

Q_H

is the heat added in the boiler. It is used to determine the efficiency of steam turbine power plants where water is the working fluid.

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